Charge trajectory calculating method, system, and program

ABSTRACT

In one embodiment, a charge trajectory calculating method of calculating, by simulation, trajectories of charges scattered by irradiating a target object with a charged beam includes setting a simulation region, which corresponds to an existence region of the target object, and retrieving measured data of a potential distribution which occurs in the target object by irradiating the target object with the charged beam, from a storage location at which the measured data is stored. The method further includes setting the measured data retrieved from the storage location, as the potential distribution which occurs in the simulation region by irradiating the simulation region with the charged beam, and calculating, by a Monte Carlo calculation, the trajectories of charges scattered by irradiating the simulation region by the charged beam, on an assumption that the measured data retrieved from the storage location is set as the potential distribution in the simulation region.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2007-29407, filed on Feb. 8,2007, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a charge trajectory calculating method,system, and program.

2. Background Art

Scanning electron microscopes (SEMs) enable observation of extremelysmall objects. The importance of the SEM technology is growing with thedevelopment of the nanotechnology. In the semiconductor industry, theSEM technology has been used for inspection and length measurement.

Recently, in the semiconductor industry, requirements on the inspectionand length measurement have become stricter as semiconductor designrules become finer. According to the strictest specification, precisionin the inspection and length measurement has to be on the order ofsub-nanometer. Further, in addition to high precision in the inspectionand length measurement, high stability in the inspection and lengthmeasurement is also required. In order to meet the requirements, it isattempted to raise resolution and stability of an SEM apparatus toimprove the hardware of an SEM, and attempted to develop such aninspection method and length measurement method as improvingreproducibility to improve the software of an SEM.

When using an SEM, SEM conditions such as accelerating voltage, samplecurrent, and bias voltage have to be optimized. Whether the SEMconditions can be appropriately optimized or not is largely dependent onthe skill of an operator. When using the SEM, the operator places ameasuring sample in the SEM, and optimizes the SEM conditions by varyingthe SEM conditions by trial and error. Optimization of the SEMconditions often takes a long time and may take several days in somecases. This has a significant effect on the turn around time (TAT) of asemiconductor manufacturing process. In the semiconductor manufacturingprocess, reduction of the TAT is imperative because the TAT has asignificant effect on the cost. It is undesirable for the semiconductormanufacturing process to take a long time to optimize the SEMconditions.

In recent years, SEM simulations using the Monte Carlo method havebecome popular. In the past, a Monte Carlo calculation required anenormously long calculation time. However, the development of theinformation processing technology in recent years has enabled the MonteCarlo calculation to be performed in a relatively short time. Accordingto an SEM simulation, the SEM conditions can be optimized without anactual measuring sample before the inspection or length measurement (seeJP-A 2002-75818 (KOKAI)).

A typical flow of the SEM simulation will be described hereinafter.

First, a simulation region which corresponds to the existence region ofa measuring object, is provided. In this step, the number of calculationmeshes in the simulation region is determined, and the calculationmeshes are provided in the simulation region. In this example, thenumber of calculation meshes in the simulation region is 9×9, i.e., 81.

Next, it is assumed that one of the meshes is irradiated with anelectron beam. Then, trajectories of scattered charges, the chargedistribution, and the potential distribution in the simulation regionare calculated. Such a calculation is repeated 81 times on theassumption that the 81 meshes are scanned (i.e., successivelyirradiated) with the electron beam. The calculation may be performed bythe two or more meshes. For example, if the calculation is performed bythe three meshes, the calculation is repeated 27 times.

The calculation of the potential distribution from the chargedistribution is performed using the Poisson equation. For thecalculation, the finite element method is often used. When calculatingthe potential distribution, charge movement has to be appropriatelytaken into account. Further, to raise precision of the calculation ofthe potential distribution, fine meshes have to be provided. However, itis difficult to meet these requirements without increasing load on acomputer and elongating time for calculating the potential distribution.

For this reason, it is attempted to perform an SEM simulation using acluster PC, which includes a plurality of PCs. The cluster PC includes,for example, a master node and a plurality of cluster nodes. The masternode generates a random number, distributes charge scatteringcalculations and charge distribution calculations among the clusternodes, collects charge information from the cluster nodes, and performspotential distribution calculations. The computational capability of thecluster PC increases as the number of the cluster nodes increases.

Exchanges of data between the master node and the cluster nodes areperformed via a network, such as a LAN. The time required for the datacommunication increases in proportion to the number of the clusternodes. As the number of the cluster nodes increases, the proportion ofthe data communication time in the entire calculation time becomesconsiderable.

As described above, the SEM simulation has a large technical problemregarding how to reduce the calculation time.

SUMMARY OF THE INVENTION

An embodiment of the present invention is, for example, a chargetrajectory calculating method of calculating, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the method comprising: setting a simulation region, whichcorresponds to the existence region of the target object; dividing thesimulation region into a plurality of segment regions; calculating, by aMonte Carlo calculation, the trajectories of charges scattered byirradiating the inside of a predetermined segment region with thecharged beam; calculating, based on the Monte Carlo calculation, thecharge distribution which occurs in the simulation region by irradiatingthe inside of the predetermined segment region with the charged beam;calculating, based on the charge distribution, the potentialdistribution which occurs in the simulation region by irradiating theinside of the predetermined segment region with the charged beam;calculating, based on the potential distribution or the chargedistribution, function values of an approximate function of thepotential distribution or the charge distribution; calculating, based onthe function values of the approximate function, the potentialdistribution which occurs in the simulation region by irradiating theoutside of the predetermined segment region with the charged beam; andcalculating, by a Monte Carlo calculation, and based on the potentialdistribution calculated based on the function values of the approximatefunction, the trajectories of charges scattered by irradiating theoutside of the predetermined segment region with the charged beam.

Another embodiment of the present invention is, for example, a chargetrajectory calculating method of calculating, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the method comprising: setting a simulation region, whichcorresponds to the existence region of the target object; retrievingmeasured data of the potential distribution which occurs in the targetobject by irradiating the target object with the charged beam, from astorage location at which the measured data is stored; setting themeasured data retrieved from the storage location, as the potentialdistribution which occurs in the simulation region by irradiating thesimulation region with the charged beam; and calculating, by a MonteCarlo calculation, the trajectories of charges scattered by irradiatingthe simulation region by the charged beam, on the assumption that themeasured data retrieved from the storage location is set as thepotential distribution in the simulation region.

Another embodiment of the present invention is, for example, a chargetrajectory calculating system for calculating, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the system comprising: a region setting section configuredto set a simulation region, which corresponds to the existence region ofthe target object; a region dividing section configured to divide thesimulation region into a plurality of segment regions; a chargetrajectory calculating section configured to calculate, by a Monte Carlocalculation, the trajectories of charges scattered by irradiating theinside of a predetermined segment region with the charged beam; a chargedistribution calculating section configured to calculate, based on theMonte Carlo calculation, the charge distribution which occurs in thesimulation region by irradiating the inside of the predetermined segmentregion with the charged beam; a potential distribution calculatingsection configured to calculate, based on the charge distribution, thepotential distribution which occurs in the simulation region byirradiating the inside of the predetermined segment region with thecharged beam; an approximate function processing section configured tocalculate, based on the potential distribution or the chargedistribution, function values of an approximate function of thepotential distribution or the charge distribution; a potentialdistribution approximating section configured to calculate, based on thefunction values of the approximate function, the potential distributionwhich occurs in the simulation region by irradiating the outside of thepredetermined segment region with the charged beam; and a chargetrajectory approximating section configured to calculate, by a MonteCarlo calculation, and based on the potential distribution calculatedbased on the function values of the approximate function, thetrajectories of charges scattered by irradiating the outside of thepredetermined segment region with the charged beam.

Another embodiment of the present invention is, for example, a chargetrajectory calculating program for making a computer perform a chargetrajectory calculating method, which calculates, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the method comprising: setting a simulation region, whichcorresponds to the existence region of the target object; dividing thesimulation region into a plurality of segment regions; calculating, by aMonte Carlo calculation, the trajectories of charges scattered byirradiating the inside of a predetermined segment region with thecharged beam; calculating, based on the Monte Carlo calculation, thecharge distribution which occurs in the simulation region by irradiatingthe inside of the predetermined segment region with the charged beam;calculating, based on the charge distribution, the potentialdistribution which occurs in the simulation region by irradiating theinside of the predetermined segment region with the charged beam;calculating, based on the potential distribution or the chargedistribution, function values of an approximate function of thepotential distribution or the charge distribution; calculating, based onthe function values of the approximate function, the potentialdistribution which occurs in the simulation region by irradiating theoutside of the predetermined segment region with the charged beam; andcalculating, by a Monte Carlo calculation, and based on the potentialdistribution calculated based on the function values of the approximatefunction, the trajectories of charges scattered by irradiating theoutside of the predetermined segment region with the charged beam.

Another embodiment of the present invention is, for example, a chargetrajectory calculating program for making a computer perform a chargetrajectory calculating method, which calculates, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the method comprising: setting a simulation region, whichcorresponds to the existence region of the target object; retrievingmeasured data of the potential distribution which occurs in the targetobject by irradiating the target object with the charged beam, from astorage location at which the measured data is stored; setting themeasured data retrieved from the storage location, as the potentialdistribution which occurs in the simulation region by irradiating thesimulation region with the charged beam; and calculating, by a MonteCarlo calculation, the trajectories of charges scattered by irradiatingthe simulation region by the charged beam, on the assumption that themeasured data retrieved from the storage location is set as thepotential distribution in the simulation region.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an SEM simulator;

FIG. 2 is a flowchart regarding an SEM simulation;

FIG. 3 is a diagram for illustrating a simulation region;

FIG. 4 is a diagram for illustrating segment regions;

FIG. 5 is a diagram for illustrating an electron trajectory calculation;

FIG. 6 shows examples of a graph of an approximate function of apotential distribution;

FIGS. 7A to 7E are diagrams for illustrating potential distributions att=a, 2a, 3a, 4a, and 5a;

FIG. 8 shows an example of an SEM image obtained by the SEM simulation;

FIG. 9 shows an example of a design pattern of a target object;

FIG. 10 is a diagram for illustrating a three-dimensional calculationmesh configuration;

FIGS. 11A to 11H are diagrams for illustrating various modifications ofsegment configuration;

FIG. 12 is a flowchart regarding a second embodiment;

FIG. 13 is a diagram for illustrating matching between SEM images; and

FIG. 14 is a flowchart regarding a third embodiment.

DESCRIPTION OF THE EMBODIMENTS First Embodiment

FIG. 1 is a functional block diagram of an SEM simulator 101 configuredto simulate an SEM measurement. The SEM simulator 101 in FIG. 1 iscapable of calculating, by simulation, trajectories of electronsscattered by irradiating a target object (measuring object) with anelectron beam. The SEM simulator 101 in FIG. 1 is a specific example ofa charge trajectory calculating system. The SEM simulator 101 in FIG. 1may be constituted by one PC or a plurality of PCs.

The SEM simulator 101 in FIG. 1 includes an arithmetic section 111, auser interface section 112, a recording section 113, and a databasesection 114. The arithmetic section 111 in FIG. 1 includes a parameterfile generating section 121, a simulation region generating section 122which is an example of a region setting section, a segment regiongenerating section 123 which is an example of a region dividing section,an electron trajectory calculating section 124 which is an example of acharge trajectory calculating section, a charge distribution calculatingsection, and a charge trajectory approximating section, and a potentialdistribution calculating section 125 which is an example of a potentialdistribution calculating section, an approximate function processingsection, and a potential distribution approximating section.

The arithmetic section 111 is a block which performs various arithmeticoperations regarding an electron trajectory calculation. The userinterface section 112 is a block through which an operator inputsvarious data required for the electron trajectory calculation, into theSEM simulator 101. For example, the operator can input variousparameters regarding the irradiation conditions of the electron beam,and various parameters regarding the physical properties of themeasuring object. Examples of the parameters include: acceleratingvoltage, electron number, scanning speed, beam diameter, and focus depthof incident electrons; various values regarding the physical propertiesof the measuring object, such as the work function, density, dielectricconstant, and mobility of the measuring object; various data regardingthe measuring object, such as plasmon scattering cross section and EBIC(electron beam induced current) image regarding the measuring object;characteristic amounts regarding the kind, composition, and structure ofthe measuring object; setting values regarding the simulation region;and the mesh size of the simulation region. The recording section 113 isa block which records results of various arithmetic operations regardingthe electron trajectory calculation. The database section 114 is a blockwhich stores data regarding a design pattern of a semiconductor device.

The parameter file generating section 121 is a block which generates aparameter file based on the data input through the user interfacesection 112. The parameter file is a data file for storing a set of datarequired for the electron trajectory calculation. Examples of the datainclude an EB parameter such as accelerating voltage and sample current,and a target object parameter such as pattern configuration andcomposition data. The generated parameter file is recorded in therecording section 113.

The simulation region generating section 122 is a block which generatesa simulation region (calculation region), which corresponds to theexistence region of the target object. The simulation region isgenerated based on the parameter file recorded in the recording section113.

The segment region generating section 123 is a block which divides thesimulation region into a plurality of segment regions (calculationsegments). The segment regions are generated based on the design patternstored in the database section 114.

The electron trajectory calculating section 124 is a block whichperforms the electron trajectory calculation based on the parameterfile, on the assumption that the simulation region is irradiated with anelectron beam. In the electron trajectory calculation, trajectories ofelectrons scattered by irradiating the simulation region with theelectron beam, are calculated by a Monte Carlo calculation. In the MonteCarlo calculation, the trajectories of scattered electrons arecalculated, and the amount of accumulated charges is calculated based onthe electron emission ratio and the number of incident electrons. Theelectron trajectory calculating section 124 calculates, based on theMonte Carlo calculation, the charge distribution which occurs in thesimulation region by irradiating the simulation region with the electronbeam. The charge distribution calculation is particularly important,when the target object is an insulator. This is because, if the targetobject is an insulator, the target object is charged by irradiating itwith the electron beam, and the electron trajectories are affectedthereby. The calculated trajectories of scattered electrons and chargedistribution are recorded in the recording section 113.

The potential distribution calculating section 125 is a block whichcalculates, based on the charge distribution, the potential distributionwhich occurs in the simulation region by irradiating the simulationregion with the electron beam. The calculation of the potentialdistribution from the charge distribution is performed using the Poissonequation. For the calculation, the finite element method can be used.The calculated potential distribution is recorded in the recordingsection 113.

FIG. 2 is a flowchart regarding an SEM simulation performed by the SEMsimulator 101.

First, the simulation region generating section 122 sets a simulationregion, and sets calculation meshes in the simulation region (S101).FIG. 3 shows 5×5 (=25) calculation meshes set in a simulation region“SIM”.

Next, the segment region generating section 123 divides the simulationregion into a plurality of segment regions (S102). FIG. 4 shows thesimulation region “SIM” divided into 5 segment regions “SEG1” to “SEG5”.

Next, the SEM simulator 101 performs an electron trajectory calculationon the assumption that the simulation region is irradiated with anelectron beam (S111 to S123). In this embodiment, as shown in FIG. 5,the electron trajectory calculation is performed on the assumption thatthe segment region “SEG1” is first scanned from left to right with theelectron beam (scanning “L1”), the segment region “SEG2” is then scannedfrom left to right with the electron beam (scanning “L2”), similarscanning is carried out for the following segment regions, and thesegment region “SEG5” is finally scanned from left to right with theelectron beam (scanning “L5”). In this embodiment, the vertical width ofeach mesh is expressed by “L”, and the scan time of each segment isexpressed by “a”.

The steps S111 to S123, in which it is assumed to irradiate thesimulation region with the electron beam, include the steps S111 to S114and the steps S121 to S123. In the steps S111 to S114, it is assumed toirradiate the inside of the segment region “SEG1”, i.e., assumed toirradiate the meshes in the segment region “SEG1”. In the steps S121 toS123, it is assumed to irradiate the outside of the segment region“SEG1”, i.e., assumed to irradiate the meshes in the segment regions“SEG2” to “SEG5”.

In the steps S111 to S114, the SEM simulator 101 calculates trajectoriesof scattered electrons, the charge distribution, and the potentialdistribution in the simulation region, on the assumption that one meshin the segment region “SEG1” is irradiated with the electron beam.

First, the electron trajectory calculating section 124 calculates, by aMonte Carlo calculation, trajectories of electrons scattered byirradiating one mesh with the electron beam (S111). Next, the electrontrajectory calculating section 124 calculates, based on the Monte Carlocalculation, the charge distribution which occurs in the simulationregion “SIM” by irradiating the mesh with the electron beam (S112).Next, the potential distribution calculating section 125 calculates,based on the charge distribution, the potential distribution whichoccurs in the simulation region “SIM” by irradiating the mesh with theelectron beam (S113). The calculation of the potential distribution fromthe charge distribution is performed using the Poisson equationrepresented as the following equation (1). In the equation (1), “ρ”denotes the charge density, “φ” denotes the potential, and “∈” denotesthe dielectric constant.

ρ=−∈∇²φ  (1)

The calculation described above is repeatedly performed five times, onthe assumption that the five meshes in the segment region “SEG1” aresuccessively irradiated with the electron beam, in other words, on theassumption that the scanning “L1” is performed (S114). As described in“Background Art”, the calculation may be performed by the two or moremeshes.

Following the steps S111 to S114, the SEM simulator 101 carries out thesteps S121 to S123. In the steps S121 to S123, the SEM simulator 101calculates the potential distribution and trajectories of scatteredelectrons in the simulation region, on the assumption that the twentymeshes in the segment regions “SEG2” to “SEG5” are successivelyirradiated with the electron beam, following the five meshes in thesegment region “SEG1”. In other words, it is assumed that the scannings“L2” to “L5” are performed following the scanning “L1”.

In this case, as the simplest method for determining the potentialdistribution, the same potential distribution as that for the segmentregion “SEG1” calculated in the steps S111 to S114 can be applied to thesegment regions “SEG2” to “SEG5”. This method can be considered to beeffective for a measuring object having a high mobility. According tothis method, the loop calculation (S111 to S114) performed in thescanning “L1” can be omitted for the scannings “L2” to “L5”, so that thetime for the SEM simulation can be substantially reduced. On the otherhand, for a measuring object having a low mobility such as an insulator,the method described below can be considered to be effective.

First, the potential distribution calculating section 125 calculates,based on the potential distribution φ (x, y) calculated in the stepsS111 to S114, function values of an approximate function P (t, x, y)that approximates the time evolution of the potential distribution φ (x,y) (S121). Here, φ (x, y) is the potential distribution in thesimulation region “SIM”, calculated in the steps S111 to S114, and P (t,x, y) is an approximate function of the potential distribution φ (x, y),which approximates the time evolution of the potential distribution φ(x, y). In the potential distribution φ (x, y) and the approximatefunction P (t, x, y), “t” denotes the time, “x” denotes thex-coordinate, and “y” denotes the y-coordinate. The approximate functionP (t, x, y) at t=a, i.e., P (a, x, y), is equal to the potentialdistribution φ (x, y). The axes of the x-coordinate and the y-coordinateare defined as shown in FIG. 5

In this embodiment, the function values of the approximate function P(t, x, y) are calculated using a differential equation containing theapproximate function P (t, x, y). More specifically, the differentialequation is a diffusion equation represented as the following equation(2), which is a partial differential equation whose variables are thetime and the coordinates, and is a kind of elliptic equation. In otherwords, the approximate function P (t, x, y) is a solution of a diffusionequation. This means that the time evolution of the potentialdistribution φ (x, y) is approximated using a diffusion equation. In theequation (2), “D” denotes the diffusion coefficient.

$\begin{matrix}{\frac{\partial P}{\partial t} = {D{\nabla^{2}P}}} & (2)\end{matrix}$

The potential distribution calculating section 125 calculates thefunction values of the approximate function P (t, x, y) by numericallysolving the diffusion equation, using the potential distribution φ (x,y) as the initial condition. Consequently, the function values of theapproximate function P (t, x, y) at various time and coordinates arecalculated. FIG. 6 shows examples of a graph of the approximate functionP (t, x, y). In this drawing, the ordinate indicates “P”, and theabscissa indicates “y”. FIG. 6 shows the approximate function P (t, x,y) at t=t1, t2, and t3 (t1<t2<t3).

The differential equation may be a partial differential equation or anelliptic equation other than the diffusion equation. In that case, themobility, dielectric constant, specific resistance or the like of themeasuring object may be taken into account as a parameter of theequation. Further, if the expression of the approximate function isavailable, the function values of the approximate function may becalculated using the expression. Examples of the expression include theexpression whose variables are time and coordinates, e.g., theexpression which is a solution of the diffusion equation.

Next, the potential distribution calculating section 125 calculates,based on the function values of the approximate function P (t, x, y),the potential distribution which occurs in the simulation region “SIM”by irradiating the inside of the segment regions “SEG2” to “SEG5”(S122). The calculation of the potential distribution will be describedwith reference to FIGS. 7A to 7E.

FIG. 7A is a diagram for illustrating the potential distribution at t=a.The potential distribution is given when the scanning “L1” is completed.The potential distribution at t=a is expressed by φ (x, y) which iscalculated in the steps S111 to S114, i.e., expressed by P (a, x, y).Therefore, at t=a, the potential in the segment region “SEG1” isexpressed by P (a, x, 0), the potential in the segment region “SEG2” isexpressed by P (a, x, L), the potential in the segment region “SEG3” isexpressed by P (a, x, 2L), and so on.

FIG. 7B is a diagram for illustrating the potential distribution att=2a. The potential distribution is given when the scanning “L2” iscompleted. The potential distribution at t=2a can be calculated bysuperimposing a first potential distribution caused by the scanning “L1”and a second potential distribution caused by the scanning “L2”. Thefirst potential distribution corresponds to the time evolution of φ (x,y), and therefore, it can be calculated by substituting t=2a into P (t,x, y). The second potential distribution corresponds to a translation ofφ (x, y), and therefore, it can be calculated by translating P (a, x, y)by “L” in the y direction. Therefore, at t=2a, the potential in thesegment region “SEG1” is expressed by P (2a, x, 0)+P (a, x, L), thepotential in the segment region “SEG2” is expressed by P (2a, x, L)+P(a, x, 0), the potential in the segment region “SEG3” is expressed by P(2a, x, 2L)+P (a, x, L), and so on.

FIG. 7C is a diagram for illustrating the potential distribution att=3a. The potential distribution is given when the scanning “L3” iscompleted. The potential distribution at t=3a can be calculated bysuperimposing a first potential distribution caused by the scanning“L1”, a second potential distribution caused by the scanning “L2”, and athird potential distribution caused by the scanning “L3”. The firstpotential distribution corresponds to the time evolution of φ (x, y),and therefore, it can be calculated by substituting t=3a into P (t, x,y). The second potential distribution corresponds to the time evolutionof a translation of φ (x, y), and therefore, it can be calculated bytranslating P (2a, x, y) by “L” in the y direction. The third potentialdistribution corresponds to a translation of φ (x, y), and therefore, itcan be calculated by translating P (a, x, y) by “2L” in the y direction.Therefore, at t=3a, the potential in the segment region “SEG1” isexpressed by P (3a, x, 0)+P (2a, x, L)+P (a, x, 2L), the potential inthe segment region “SEG2” is expressed by P (3a, x, L)+P (2a, x, 0)+P(a, x, L), the potential in the segment region “SEG3” is expressed by P(3a, x, 2L)+P (2a, x, L)+P (a, x, 0), and so on.

Similarly, the potential distribution at t=4a is given as shown in FIG.7D, and the potential distribution at t=5a is given as shown in FIG. 7E.In this way, the potential distribution at t=5a, i.e., the potentialdistribution which occurs in the simulation region “SIM” by irradiatingthe segment regions “SEG2” to “SEG5”, is calculated. The potentialdistribution at t=5a is the potential distribution which occurs finallyin the simulation region “SIM” by irradiating the simulation region“SIM” with the electron beam. This potential distribution occurs in thesimulation region “SIM” by irradiating the segment regions “SEG2” to“SEG5”, following the segment region “SEG1”.

The potential distribution calculating section 125 calculates thepotential distribution at t=5a, as the potential distribution whichoccurs in the simulation region “SIM” by irradiating the segment regions“SEG2” to “SEG5”. The potential distribution calculating section 125need not calculate the potential distributions at t=2a, 3a, and 4a, andis needed only to calculate the potential distribution at t=5a. Tocalculate the potential distribution at t=5a, the function values of theapproximate function P (t, x, y) shown in FIG. 7E are needed. Moreprecisely, the function values of the approximate function P (t, x, y)shown in FIG. 7E into which x=0, L, 2L, 3L, and 4L are substituted areneeded. The potential distribution calculating section 125 calculatesthese values required for the calculation in the step S122, in the stepS121.

Next, the electron trajectory calculating section 124 calculates, by aMonte Carlo calculation, and based on the potential distributioncalculated base on the function values of the approximate function P (t,x, y), trajectories of electrons scattered by irradiating the segmentregions “SEG2” to “SEG5” with the electron beam (S123). In this way, thetrajectories of electrons scattered by irradiating the segment regions“SEG2” to “SEG5” following the segment region “SEG1”, are calculated.

The electron trajectory calculating section 124 can calculate an SEMimage, based on the trajectories of scattered electrons calculated inthe step S123. FIG. 8 shows an example of such an SEM image. As a designpattern of the target object, the pattern shown in FIG. 9 is assumed.Peaks in FIG. 8 reflect the edges of “H” parts (high parts) in FIG. 9,and valleys in FIG. 8 reflect “L” parts (low parts) in FIG. 9.

The SEM simulation according to this embodiment has been describedabove. In this embodiment, the electron trajectory calculation regardingthe scannings “L2” to “L5” is performed not by the same loop calculationas that for the scanning “L1” (S111 to S114), but by the simplerapproximate calculation (S121 to S123). Consequently, in thisembodiment, the time for the SEM simulation can be substantiallyreduced.

This embodiment is particularly advantageous when the SEM simulation isperformed by a cluster PC. According to this embodiment, the amount ofdata exchanged between a master node and a cluster node is reduced, inthe electron trajectory calculation regarding the scannings “L2” to“L5”. This is because the amount of the calculation regarding theelectron scattering is reduced and the calculation of the chargedistribution is not needed. Consequently, in this embodiment, the timefor the SEM simulation can be further reduced.

This embodiment can also be applied to a charged beam other than theelectron beam. Examples of such a charged beam include an ion beam.

The approximate function in the steps S121 to S123 may be an approximatefunction that approximates the time evolution of the chargedistribution. In this case, in the step S121, the function values of theapproximate function of the charge distribution is calculated based onthe charge distribution calculated in the steps S111 to S114. In thestep S122, the charge distribution which occurs by irradiating theinside of the segment regions “SEG2” to “SEG5” is calculated based onthe function values of the approximate function of the chargedistribution. Then, the potential distribution calculating section 125calculates, based on the charge distribution, the potential distributionwhich occurs by irradiating the segment regions “SEG2” to “SEG5” withthe electron beam. The calculation of the potential distribution fromthe charge distribution is performed using the Poisson equationdescribed above. Then, in the step S123, trajectories of electronsscattered by irradiating the segment regions “SEG2” to “SEG5” by theelectron beam is calculated by a Monte Carlo calculation and based onthe potential distribution.

Further, in this embodiment, the calculation meshes can be configuredthree-dimensionally rather than two-dimensionally.

When the two-dimensional mesh configuration is employed, the linearsegments as shown in FIG. 4 can be employed for example. Examples of thetwo-dimensional meshes include triangular meshes, quadrangular meshes,and hybrid meshes including various polygonal meshes. On the other hand,when the three-dimensional mesh configuration is employed, the planarsegments as shown in FIG. 10 can be employed for example. Examples ofthe three-dimensional meshes include tetrahedral meshes, hexahedralmeshes, and hybrid meshes including various polyhedral meshes.

Other various modifications of the segment configuration are possible.In the following, various modifications of the segment configurationwill be described.

FIG. 11A shows an example of a periodic design pattern. The designpattern includes a line pattern in which five lines extending in they-direction occur periodically in the x-direction. The scanningdirection of the electron beam is the x-direction, as in the embodimentdescribed above.

FIG. 11B shows an example of a segment configuration in this case. InFIG. 11B, the simulation region is divided into seven linear segmentregions “SEG1” to “SEG7” extending in the x-direction. Each segmentregion is a region to be scanned in one scanning (scanning region). Thatis, in FIG. 11B, the simulation region is divided into segment regionsby the scanning region. In this case, the electron trajectorycalculation can be performed, for example, by extrapolating the resultof the loop calculation for the segment region “SEG1” to the segmentregions “SEG2” to “SEG7”, as in the embodiment described above.

FIG. 11C shows another example of the segment configuration. In FIG.11C, each segment region shown in FIG. 11B is further divided equallyinto two. That is, while one segment region is provided in each scanningregion in FIG. 11B, a plurality of (two in this example) segment regionsare provided in each scanning region in FIG. 11C. This configuration isprovided in consideration for the linear symmetry of the design patternshown in FIG. 11A with regard to the centerline. In this case, theelectron trajectory calculation can be performed, for example, byextrapolating the result of the loop calculation for the segment region“SEG1” to the segment regions “SEG2” to “SEG14”. In this case, the timefor the SEM simulation is reduced compared with the case shown in FIG.11B.

FIG. 11D shows another example of the segment configuration. In FIG.11D, each segment region shown in FIG. 11B is further divided equallyinto five. In this case, the electron trajectory calculation can beperformed, for example, by extrapolating the result of the loopcalculation for the segment region “SEG1” to the segment regions “SEG5”,“SEG6”, “SEG10” and the like, and extrapolating the result of the loopcalculation for the segment region “SEG2” to the segment regions “SEG3”,“SEG4”, “SEG7”, “SEG8”, “SEG9” and the like. In this case, the time forthe SEM simulation is reduced compared with the cases shown in FIGS. 11Band 11C. The loop calculations are performed for the segment regions“SEG1” and “SEG2” in this case, because the charged state of thesimulation region often differs between the inside and the periphery ofthe simulation region. To further raise the calculation precision, theelectron trajectory calculation can be performed, for example, byextrapolating the result of the loop calculation for the segment region“SEG1” to the segment regions “SEG5”, “SEG6”, “SEG10” and the like,extrapolating the result of the loop calculation for the segment region“SEG2” to the segment regions “SEG4”, “SEG7”, “SEG9” and the like, andextrapolating the result of the loop calculation for the segment region“SEG3” to the segment regions “SEG8” and the like. In this way, it isimportant that the division of the simulation region and the selectionof the segment regions for which the loop calculations are performed arecarried out in view of the calculation precision.

FIG. 11E shows an example of a non-periodic design pattern. The designpattern shown in FIG. 11E includes a pattern in which a structure “X”disturbing the periodicity is placed in the design pattern shown in FIG.11A. The scanning direction of the electron beam is the x-direction, asin the embodiment described above.

FIG. 11F shows an example of a segment configuration in this case. InFIG. 11F, the simulation region is divided into seven linear segmentregions “SEG1” to “SEG7” extending in the x-direction, as in FIG. 11B.The structure “X” exists in the segment region “SEG4”. In FIG. 11F, thesimulation region is divided into the segment regions “SEG1” to “SEG3”and “SEG5” to “SEG7”, each of which has a periodic pattern, and thesegment region “SEG4”, which has a non-periodic pattern. In this case,the electron trajectory calculation can be performed, for example, byextrapolating the result of the loop calculation for the segment region“SEG1” to the segment regions “SEG2” to “SEG3” and “SEG5” to “SEG7”, andseparately performing the electron trajectory calculation for thesegment region “SEG4”. In this example, the number of segment regionshaving a periodic pattern is six, and the number of segment regionshaving a non-periodic pattern is one. However, the number of the segmentregions having a periodic pattern and the number of the segment regionshaving a non-periodic pattern can be arbitrarily determined.

FIG. 11G shows a further example of a design pattern. The design patternincludes a pattern “A” and a pattern “B”. The scanning direction of theelectron beam is the x-direction, as in the embodiment described above.

In this case, the simulator 101 may automatically group the segmentregions based on contour data of the design data. The automatic groupingis achieved, for example, by extracting vector components. The simulator101 extracts vector components from the contour data regarding thepatterns “A” and “B”, and automatically groups the segment regions basedon the vector components.

FIG. 11H shows an example of such grouping. In FIG. 11H, the segmentregions that are equivalent in vector components in the meshes aregrouped into the same group. In FIG. 11H, seven segment regions aregrouped into a group “A”, a group “B”, and a group “C” according to thevector components in the x-direction. In the grouping, the vectorcomponents in the x-direction are used. However, the vector componentsin the y-direction may be used.

The electron trajectory calculation is performed for each group. Theresult of the loop calculation for one segment region in the group “A”is extrapolated to other segment regions in the group “A”. The result ofthe loop calculation for one segment region in the group “B” isextrapolated to other segment regions in the group “B”.

Various modifications of the segment configuration have been described.In addition, as an electron trajectory calculation method, extrapolationof the result of the loop calculation for a predetermined segment region(a segment region for which the loop calculation is to be performed) toother segment regions has been described. The number of segment regionsfor which the loop calculation is to be performed may be two or more. Toreduce the time for the electron trajectory calculation, it is importantthat each segment region is as small as possible in view of thecharacteristics of the design pattern and the required calculationprecision.

Second Embodiment

In the first embodiment, there has been described a method ofcalculating a potential distribution or a charge distribution based onfunction values of an approximate function. The approximate function mayinclude a coefficient which originates from a coefficient in adifferential equation or an expression. Examples of such a coefficientinclude the diffusion coefficient of the diffusion equation.

To calculate the function values of the approximate function, the valueof the coefficient of the approximate function has to be previouslydetermined. In the first embodiment, it is assumed that a knownexperimental value is used as the value of the coefficient of theapproximate function. However, the simulation using the knownexperimental value may provide an incorrect result. Therefore, in thesecond embodiment, a value automatically determined by the simulator 101is used as the value of the coefficient of the approximate function.Therefore, according to the second embodiment, a coefficient value thatprovides a correct simulation result can be determined.

In the following, with reference to FIG. 12, a method of automaticallydetermining the value of the coefficient of the approximate functionwill be described.

First, the simulator 101 temporarily sets a value of the coefficient ofthe approximate function (S201). Specifically, for example, a parameter(the setting range, the step size, or the like) for temporarily settingthe coefficient value is set, and the coefficient value is set based onthe parameter.

Next, the simulator 101 performs the electron trajectory calculationshown in the steps S101 to S123 in FIG. 2, using the coefficient value(S202). Next, the simulator 101 calculates the SEM image of themeasuring object, based on the result of the electron trajectorycalculation (S203).

Next, the simulator 101 compares the SEM image obtained by thecalculation with an SEM image obtained by an experiment (S204). For thecomparison of the SEM images, image matching between the SEM images canbe used, for example. As shown in FIG. 13, the simulator 101superimposes the SEM images (secondary electron profiles) on oneanother, calculates the difference between them, and determines whetherthe resulting difference value (GOF value) is less than a threshold ornot.

If the difference value is equal to or more than the threshold (S205),the simulator 101 performs the steps S201 to S204 again. In this case,the value of the coefficient of the approximate function is changed. Onthe other hand, if the difference value is less than the threshold(S205), the simulator 101 designates the temporarily set value in S201,as the value of the coefficient of the approximate function (S206). Inthis way, the simulator 101 determines the value of the coefficient ofthe approximate function, based on the result of the comparison betweenthe SEM images.

In the step S204, the SEM image obtained in the steps S201 to S203 iscompared with the SEM image obtained previously. In this example, thelatter SEM image is an SEM image obtained experimentally. However, thelatter SEM image may be an SEM image obtained by another SEM simulationmethod.

The simulator 101 may perform the steps S201 to S204 for all thecoefficient values in the setting range. In this case, the simulator 101may designate the coefficient value that provides the smallestdifference value, as the value of the coefficient of the approximatefunction (S205 to S206). In this case, the steps S201 to S204 areperformed for each of the coefficient values.

The data to be compared in the step S204 may be shape data other thanthe SEM image. For example, the distance between lines formed on themeasuring object may be used. Instead of the SEM image itself, theamplitude of the peak of the SEM image, the width of the peak of the SEMimage, the ratio between the amplitude and the width, or the contrastratio based on the data about the peak and the valley of the SEM imagemay be used. In this case, a calculation for obtaining such shape datais performed in the step S203.

Third Embodiment

In the first embodiment, trajectories of scattered electrons arecalculated using the potential distribution obtained by calculation. Onthe other hand, in the third embodiment, trajectories of scatteredelectrons are calculated using previously prepared measured data of thepotential distribution. Therefore, according to the third embodiment,the time for the SEM simulation can be substantially reduced. Examplesof the potential measuring method include a potential measuring methodusing the correlation between the sample surface potential and the focusvalue in the SEM apparatus, a surface potential measuring method usingKFM, and a potential measuring method using a capacitance sensor.

FIG. 14 is a flowchart regarding the SEM simulation according to thisembodiment.

First, the simulation region generating section 122 sets a simulationregion, and sets calculation meshes in the simulation region (S301).This step is same as the step S101 in FIG. 2.

Next, the potential distribution calculating section 125 retrievesmeasured data of the potential distribution, from a storage location atwhich the measured data is stored (S302). The measured data ispreviously obtained by potential distribution measurement for a targetobject of the SEM simulation. In other words, the measured data ispreviously obtained by measuring the potential distribution which occursin the target object by irradiating the target object with an electronbeam. In this embodiment, the storage location is the database section114 shown in FIG. 1.

Next, the potential distribution calculating section 125 sets themeasured data retrieved from the storage location, as the potentialdistribution which occurs in the simulation region by irradiating thesimulation region with the electron beam (S303).

Next, the electron trajectory calculating section 124 calculates, by aMonte Carlo calculation, trajectories of electrons scattered byirradiating the simulation region with the electron beam, on theassumption that the measured data retrieved from the storage location isset as the potential distribution in the simulation region (S304).

The SEM simulation process performed by the SEM simulator 101 in thefirst to third embodiments can be performed by a computer program (acharge trajectory calculating program), for example. The program isstored in a storage in the SEM simulator 101 and executed by a processorin the SEM simulator 101, for example.

As described above, with regard to a charge trajectory calculatingmethod, system, and program that calculate, by simulation, trajectoriesof charges scattered by irradiating a target object with a charged beam,the embodiments of the present invention can reduce the calculationtime.

1.-15. (canceled)
 16. A charge trajectory calculating method ofcalculating, by simulation, trajectories of charges scattered byirradiating a target object with a charged beam, the method comprising:setting a simulation region, which corresponds to an existence region ofthe target object; retrieving measured data of a potential distributionwhich occurs in the target object by irradiating the target object withthe charged beam, from a storage location at which the measured data isstored; setting the measured data retrieved from the storage location,as the potential distribution which occurs in the simulation region byirradiating the simulation region with the charged beam; andcalculating, by a Monte Carlo calculation, the trajectories of chargesscattered by irradiating the simulation region by the charged beam, onan assumption that the measured data retrieved from the storage locationis set as the potential distribution in the simulation region. 17.-19.(canceled)
 20. A computer readable record medium storing a chargetrajectory calculating program for making a computer perform a chargetrajectory calculating method, which calculates, by simulation,trajectories of charges scattered by irradiating a target object with acharged beam, the method comprising: setting a simulation region, whichcorresponds to an existence region of the target object; retrievingmeasured data of a potential distribution which occurs in the targetobject by irradiating the target object with the charged beam, from astorage location at which the measured data is stored; setting themeasured data retrieved from the storage location, as the potentialdistribution which occurs in the simulation region by irradiating thesimulation region with the charged beam; and calculating, by a MonteCarlo calculation, the trajectories of charges scattered by irradiatingthe simulation region by the charged beam, on an assumption that themeasured data retrieved from the storage location is set as thepotential distribution in the simulation region.